4-bet shove looks pretty strong especially from BB. SB can easily be trying to iso the aggro big stack with a medium Ace, or suited broadways, or is just fed up with the big stack's aggresion. Sb would shove any small to medium PP, so the most feared hands are QQ+, which is not that bad, because you got 2 blockers and even vs. KK you got 65% equity. You could be called with 99-JJ but this is OK because of the dead money (assuming Co folding in at least 80%).
Add your tightish image to the equation and it shold be a profitable move.
Another argument is that you can be call very light by SB with hands you easily dominate, especially Ax.
Ship it and embrace variance